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Basketball by the numbers: an introduction featuring Kyrie Irving

Using Game 5 of the Finals to explain some basic stats.

NBA: Finals-Cleveland Cavaliers at Golden State Warriors Bob Donnan-USA TODAY Sports

You can find an overwhelming amount of numbers regarding the game of basketball. But what do they all mean? How important is each one? How do they relate to each other? I’ll explore the answers to questions like these in this weekly column, along with other statistically-oriented topics.

What is the most basic, most important number in basketball? Points. If one team scored 110 points and the other scored 103 points, then the team which scored 110 points wins the game regardless of what any other numbers say.

Sometimes, people might argue that the losing team should've won based on one number or another. But in the words of Jim Boeheim, "That's why they make scoreboards."

Therefore, for any other number to have meaning, it must be related to points in some way. Without that context it doesn't have any meaning.

What component parts are necessary to calculate the number of points scored in a game?

PTS = (2P * 2) + (3P * 3) + FT

[PTS points; 2P 2-point field goals; 3P 3-point field goals; FT free throws].

(Note: There is an excellent glossary of basketball abbreviations on

These are the three methods of scoring points, and therefore are next most important numbers in basketball. We’ll examine each of them in detail in future installments.

However, each team gets roughly the same number of possessions in a game, which means they have about the same number of opportunities to score points. Therefore using these opportunities efficiently is of paramount importance. How can we measure efficiency? There are two aspects we must consider:

1. Shooting efficiency

Shooting efficiency = PTS/TSA

[TSA true shot attempts].

What is a true shot attempt? Every two point attempt or three point attempt counts as one true shot attempt. Free throw attempts are where things get tricky, as there are several different scenarios that must be accounted for:

  1. Free throws resulting from a shooting foul on a missed two point shot counts as one true shot attempt for both free throw attempts.
  2. Free throws resulting from a shooting foul on a missed three point shot count as one true shot attempt for all three free throw attempts.
  3. Free throws resulting from a shooting foul on a made shot (also known as an "and-one") do not count as a true shot attempt, as it is already recorded for the made field goal.
  4. Free throws resulting from technical or flagrant do not count as a true shot attempt, as these are extra.

Of course, since data regarding the various situations which can result in free throws is not readily available at this time an estimate is typically used. Thus, the formula to calculate true shot attempts for a player or a team is TSA = FGA + (FTA * 0.44).

[FGA field goal attempts; FTA free throw attempts].

Let’s try all this out. In Game 5 of the NBA Finals, vs. the Warriors Kyrie Irving made 12 2-pointers, five 3-pointers and two free throws. Plugging these numbers into the points formula we get:

PTS = (2P * 2) + (3P * 3) + FT

PTS = (12 * 2) + (5 * 3) + 2

PTS = 24 + 15 + 2

PTS = 41

Irving had 24 field goal attempts in this game, along with two free throw attempts. Using the true shooting attempts formula we get:

TSA = FGA + (FTA * 0.44)

TSA = 24 + (2 * 0.44)

TSA = 24 + 0.88

TSA = 24.88

TSA ≈ 25

In this case, from looking at the play-by-play, we can learn that both of Irving’s free throw attempts were the result of and-ones, so technically neither should count as a true shot attempt. But since the point of this exercise is to learn the formula to estimate true shot attempts, we’ll stick with the 25 figure that the formula produced. Now that we have both necessary components we can calculate Irving’s shooting efficiency from that game:

Shooting efficiency = PTS / TSA

Shooting efficiency = 41 / 25

Shooting efficiency = 1.64

So Irving produced 1.64 points per true shot attempt during that game. This is the highest shooting efficiency of any 40 point game in the NBA Finals since the the 3-point line was introduced during the 1979-80 season.

In upcoming weeks we’ll take a deeper look at the many factors which impact shooting efficiency, including shot creation, shot distribution and spacing.

2. Possession efficiency

Not every possession results in exactly one shot attempt. Some possessions end before a shot can be taken, while others continue after a shot is missed. Each offensive rebound is worth +1 shot attempt, while each turnover is worth -1 shot attempt.

Possession efficiency = ORB - TOV

[ORB offensive rebounds; TOV turnovers].

During Game 3 of the 2016 NBA Finals, the Cavaliers had 17 offensive rebounds and 13 turnovers in a 94 possession game. Using the above formula we can calculate their possession efficiency:

Possession efficiency = ORB - TOV

Possession efficiency = 17 - 13

Possession efficiency = +4

This means that during that 94 possession game Cleveland managed to get off 98 true shot attempts.* That’s quite an accomplishment, as the league average last season was -4. Meanwhile, the Golden State Warriors had eight offensive rebounds and 18 turnovers:

Possession efficiency = ORB - TOV

Possession efficiency = 8 - 18

Possession efficiency = -10

So while Cleveland managed 98 true shot attempts Golden State could only muster 84. Even if Golden State had shot the lights out during this game, they would’ve been hard pressed to overcome such a drastic deficit in possession efficiency. And it was actually Cleveland that shot the lights out while Golden State struggled from the field, resulting in a 30-point blowout.

I hope you enjoyed the maiden voyage of Basketball by the numbers. Next week we’ll dig deeper into possession efficiency. And while I have several other topics in mind for future weeks, I’d love to hear some suggestions from readers about statistics you’d like to learn more about. Please share your ideas in the comments below, or if you’re feeling adventurous you can tweet me @EVR1022. It should be noted that I have no followers and don’t actually tweet anything. I just lurk and follow a bunch of NBA news-breakers. But if you tweet at me I will read it and take your suggestion into consideration, even though I may not respond.

* While accurate in this case, this formula isn’t always precise because of the way the NBA records team rebounds, as we’ll discuss in more detail next week. But it gets you close, and the concept of using possessions efficiently is what really matters here.